This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A157834 #25 Sep 08 2022 08:45:42
%S A157834 3,5,7,13,15,23,27,33,35,37,43,55,65,75,77,93,103,105,117,127,133,147,
%T A157834 153,155,163,167,205,215,225,247,253,257,275,285,287,293,295,303,313,
%U A157834 323,337,363,365,405,427,433,435,475,477,483,495,497,517
%N A157834 Numbers n such that 3n-2 and 3n+2 are both prime.
%C A157834 Barycenter of cousin primes (A029708; see also A029710, A023200, A046132), divided by 3. When p>3 and p+4 both are prime, then p = 1 (mod 6) and p+2 = 3 (mod 6). - _M. F. Hasler_, Jan 14 2013
%H A157834 Robert Israel, <a href="/A157834/b157834.txt">Table of n, a(n) for n = 1..10000</a>
%F A157834 Intersection of A024893 and A153183.
%F A157834 a(n) = A029708(n)/3. - _Zak Seidov_, Aug 07 2009
%F A157834 a(n) = A056956(n)*2+1 = (A029710(n)+2)/3 = (A023200(n+1)+2)/3. - _M. F. Hasler_, Jan 14 2013
%e A157834 15*3 +/- 2 = 43,47 (both prime).
%p A157834 select(t -> isprime(3*t+2) and isprime(3*t-2), [seq(t,t=3..1000,2)]); # _Robert Israel_, May 28 2017
%t A157834 Select[Range[600],AllTrue[3#+{2,-2},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Feb 03 2019 *)
%o A157834 (Magma) [n: n in [1..1000]|IsPrime(3*n-2)and IsPrime(3*n+2)] // _Vincenzo Librandi_, Dec 13 2010
%Y A157834 Intersection of A024893 and A153183.
%K A157834 nonn
%O A157834 1,1
%A A157834 _Kyle D. Balliet_, Mar 07 2009